%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU323+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 08:53:38 PM UTC 2025
% Result : Theorem 6.91s 2.66s
% Output : CNFRefutation 7.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 89 ( 39 ~; 33 |; 7 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > open_subset > element > closed_subset > topological_space > top_str > one_sorted_str > topstr_closure > subset_complement > interior > #nlpp > the_carrier > powerset > #skF_5 > #skF_4 > #skF_1 > #skF_7 > #skF_6 > #skF_2 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(topstr_closure,type,
topstr_closure: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(the_carrier,type,
the_carrier: $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(open_subset,type,
open_subset: ( $i * $i ) > $o ).
tff(one_sorted_str,type,
one_sorted_str: $i > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(closed_subset,type,
closed_subset: ( $i * $i ) > $o ).
tff(interior,type,
interior: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff(topological_space,type,
topological_space: $i > $o ).
tff(top_str,type,
top_str: $i > $o ).
tff(f_127,negated_conjecture,
~ ! [A] :
( ( topological_space(A)
& top_str(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> open_subset(interior(A,B),A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tops_1) ).
tff(f_57,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
tff(f_49,axiom,
! [A,B] :
( element(B,powerset(A))
=> ( subset_complement(A,subset_complement(A,B)) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
tff(f_117,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_1) ).
tff(f_63,axiom,
! [A,B] :
( ( top_str(A)
& element(B,powerset(the_carrier(A))) )
=> element(topstr_closure(A,B),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
tff(f_72,axiom,
! [A,B] :
( ( topological_space(A)
& top_str(A)
& element(B,powerset(the_carrier(A))) )
=> closed_subset(topstr_closure(A,B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_tops_1) ).
tff(f_110,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
tff(f_36,axiom,
! [A,B] :
( ( topological_space(A)
& top_str(A)
& closed_subset(B,A)
& element(B,powerset(the_carrier(A))) )
=> open_subset(subset_complement(the_carrier(A),B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_tops_1) ).
tff(c_52,plain,
top_str('#skF_6'),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_50,plain,
element('#skF_7',powerset(the_carrier('#skF_6'))),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_14,plain,
! [A_9,B_10] :
( element(subset_complement(A_9,B_10),powerset(A_9))
| ~ element(B_10,powerset(A_9)) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_90,plain,
! [A_42,B_43] :
( ( subset_complement(A_42,subset_complement(A_42,B_43)) = B_43 )
| ~ element(B_43,powerset(A_42)) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_102,plain,
subset_complement(the_carrier('#skF_6'),subset_complement(the_carrier('#skF_6'),'#skF_7')) = '#skF_7',
inference(resolution,[status(thm)],[c_50,c_90]) ).
tff(c_490,plain,
! [A_79,B_80] :
( ( subset_complement(the_carrier(A_79),topstr_closure(A_79,subset_complement(the_carrier(A_79),B_80))) = interior(A_79,B_80) )
| ~ element(B_80,powerset(the_carrier(A_79)))
| ~ top_str(A_79) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_538,plain,
( ( subset_complement(the_carrier('#skF_6'),topstr_closure('#skF_6','#skF_7')) = interior('#skF_6',subset_complement(the_carrier('#skF_6'),'#skF_7')) )
| ~ element(subset_complement(the_carrier('#skF_6'),'#skF_7'),powerset(the_carrier('#skF_6')))
| ~ top_str('#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_490]) ).
tff(c_542,plain,
( ( subset_complement(the_carrier('#skF_6'),topstr_closure('#skF_6','#skF_7')) = interior('#skF_6',subset_complement(the_carrier('#skF_6'),'#skF_7')) )
| ~ element(subset_complement(the_carrier('#skF_6'),'#skF_7'),powerset(the_carrier('#skF_6'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_538]) ).
tff(c_608,plain,
~ element(subset_complement(the_carrier('#skF_6'),'#skF_7'),powerset(the_carrier('#skF_6'))),
inference(splitLeft,[status(thm)],[c_542]) ).
tff(c_611,plain,
~ element('#skF_7',powerset(the_carrier('#skF_6'))),
inference(resolution,[status(thm)],[c_14,c_608]) ).
tff(c_618,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_611]) ).
tff(c_620,plain,
element(subset_complement(the_carrier('#skF_6'),'#skF_7'),powerset(the_carrier('#skF_6'))),
inference(splitRight,[status(thm)],[c_542]) ).
tff(c_16,plain,
! [A_11,B_12] :
( element(topstr_closure(A_11,B_12),powerset(the_carrier(A_11)))
| ~ element(B_12,powerset(the_carrier(A_11)))
| ~ top_str(A_11) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_48,plain,
~ open_subset(interior('#skF_6','#skF_7'),'#skF_6'),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_54,plain,
topological_space('#skF_6'),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_20,plain,
! [A_13,B_14] :
( closed_subset(topstr_closure(A_13,B_14),A_13)
| ~ element(B_14,powerset(the_carrier(A_13)))
| ~ top_str(A_13)
| ~ topological_space(A_13) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_628,plain,
( closed_subset(topstr_closure('#skF_6',subset_complement(the_carrier('#skF_6'),'#skF_7')),'#skF_6')
| ~ top_str('#skF_6')
| ~ topological_space('#skF_6') ),
inference(resolution,[status(thm)],[c_620,c_20]) ).
tff(c_645,plain,
closed_subset(topstr_closure('#skF_6',subset_complement(the_carrier('#skF_6'),'#skF_7')),'#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_52,c_628]) ).
tff(c_42,plain,
! [A_24,B_25] :
( subset(A_24,B_25)
| ~ element(A_24,powerset(B_25)) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_648,plain,
subset(subset_complement(the_carrier('#skF_6'),'#skF_7'),the_carrier('#skF_6')),
inference(resolution,[status(thm)],[c_620,c_42]) ).
tff(c_44,plain,
! [A_24,B_25] :
( element(A_24,powerset(B_25))
| ~ subset(A_24,B_25) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_101,plain,
! [B_25,A_24] :
( ( subset_complement(B_25,subset_complement(B_25,A_24)) = A_24 )
| ~ subset(A_24,B_25) ),
inference(resolution,[status(thm)],[c_44,c_90]) ).
tff(c_2605,plain,
! [A_134,A_135] :
( ( subset_complement(the_carrier(A_134),topstr_closure(A_134,A_135)) = interior(A_134,subset_complement(the_carrier(A_134),A_135)) )
| ~ element(subset_complement(the_carrier(A_134),A_135),powerset(the_carrier(A_134)))
| ~ top_str(A_134)
| ~ subset(A_135,the_carrier(A_134)) ),
inference(superposition,[status(thm),theory(equality)],[c_101,c_490]) ).
tff(c_2666,plain,
( ( subset_complement(the_carrier('#skF_6'),topstr_closure('#skF_6',subset_complement(the_carrier('#skF_6'),'#skF_7'))) = interior('#skF_6',subset_complement(the_carrier('#skF_6'),subset_complement(the_carrier('#skF_6'),'#skF_7'))) )
| ~ element('#skF_7',powerset(the_carrier('#skF_6')))
| ~ top_str('#skF_6')
| ~ subset(subset_complement(the_carrier('#skF_6'),'#skF_7'),the_carrier('#skF_6')) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_2605]) ).
tff(c_2694,plain,
subset_complement(the_carrier('#skF_6'),topstr_closure('#skF_6',subset_complement(the_carrier('#skF_6'),'#skF_7'))) = interior('#skF_6','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_648,c_52,c_50,c_102,c_2666]) ).
tff(c_2,plain,
! [A_1,B_2] :
( open_subset(subset_complement(the_carrier(A_1),B_2),A_1)
| ~ element(B_2,powerset(the_carrier(A_1)))
| ~ closed_subset(B_2,A_1)
| ~ top_str(A_1)
| ~ topological_space(A_1) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_2744,plain,
( open_subset(interior('#skF_6','#skF_7'),'#skF_6')
| ~ element(topstr_closure('#skF_6',subset_complement(the_carrier('#skF_6'),'#skF_7')),powerset(the_carrier('#skF_6')))
| ~ closed_subset(topstr_closure('#skF_6',subset_complement(the_carrier('#skF_6'),'#skF_7')),'#skF_6')
| ~ top_str('#skF_6')
| ~ topological_space('#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_2694,c_2]) ).
tff(c_2794,plain,
( open_subset(interior('#skF_6','#skF_7'),'#skF_6')
| ~ element(topstr_closure('#skF_6',subset_complement(the_carrier('#skF_6'),'#skF_7')),powerset(the_carrier('#skF_6'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_52,c_645,c_2744]) ).
tff(c_2795,plain,
~ element(topstr_closure('#skF_6',subset_complement(the_carrier('#skF_6'),'#skF_7')),powerset(the_carrier('#skF_6'))),
inference(negUnitSimplification,[status(thm)],[c_48,c_2794]) ).
tff(c_2803,plain,
( ~ element(subset_complement(the_carrier('#skF_6'),'#skF_7'),powerset(the_carrier('#skF_6')))
| ~ top_str('#skF_6') ),
inference(resolution,[status(thm)],[c_16,c_2795]) ).
tff(c_2810,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_620,c_2803]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU323+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 22:48:51 EDT 2025
% 0.13/0.34 % CPUTime :
% 6.91/2.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.91/2.66
% 6.91/2.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------